However, Sami appealed both her conviction and sentence to the Court of Appeal, claiming she was the victim of a miscarriage of justice.
Her lawyer, Jonathan Eaton QC, argued there was a lack of "essential balance" in the summing-up at the trial's conclusion.
The Crown in its closing address to the jury said fatal head injuries from low falls were rare and referred to a statistic from evidence that it was a "one in two million" occurrence.
Eaton said the figure was meaningless, it should never have been mentioned by the Crown, and it was not properly dealt with by Justice Rachel Dunningham.
He also claimed there had been an improper reliance by the Crown, not corrected, on common sense and life experience when the trial had in fact been "a contest of experts", and there was inadequate assistance from the judge on the expert evidence.
Eaton claimed the failures had led to a miscarriage of justice.
He also said new US forensic pathologist evidence, which had become available since the trial, supported the defence case that the facial bruising could have been caused by medical procedures, especially during the attempted resuscitation of the child.
But in a newly released judgement, Court of Appeal judges declined an application to adduce further evidence, while also dismissing the appeal against conviction.
The appeal judges did, however, accept that Sami's final sentence of five years' jail was too long.
They quashed the five-year sentence and replaced it with one of four and a half years' imprisonment after finding that Sami "did present a distinctive combination of factors" that merited a shorter sentence, including the fact she was separated from her very young child, that English was not her first language, her youth, and her family being in Fiji.
"We recognise she is not without support in New Zealand, and that perhaps it was to be her permanent home, but this package of factors leads us to consider further credit was appropriate," the Court of Appeal concluded.
